Interacting dimers on the honeycomb lattice: An exact solution of the five-vertex model

TL;DR

This paper extends the exact solution of close-packed dimers on the honeycomb lattice to include interactions, revealing new phases and phase transitions using Bethe ansatz and five-vertex model techniques.

Contribution

It provides an exact solution for interacting dimers on the honeycomb lattice and maps out the complete phase diagram including new frozen phases.

Findings

A new frozen phase with attractive interactions emerges.

A first-order transition line separates two frozen phases for repulsive interactions.

Critical behavior remains the same as noninteracting case with specific heat exponent 1/2.

Abstract

The problem of close-packed dimers on the honeycomb lattice was solved by Kasteleyn in 1963. Here we extend the solution to include interactions between neighboring dimers in two spatial lattice directions. The solution is obtained by using the method of Bethe ansatz and by converting the dimer problem into a five-vertex problem. The complete phase diagram is obtained and it is found that a new frozen phase, in which the attracting dimers prevail, arises when the interaction is attractive. For repulsive dimer interactions a new first-order line separating two frozen phases occurs. The transitions are continuous and the critical behavior in the disorder regime is found to be the same as in the case of noninteracting dimers characterized by a specific heat exponent $\a=1/2$.